Smoothness of the law of the supremum of the fractional Brownian motion
Noureddine Lanjri Zaïdi, Université Ibn Tofaïl, Kénitra, Maroc
David Nualart, Universitat de Barcelona
Abstract
This note is devoted to prove that the supremum of a fractional Brownian
motion with Hurst parameter $Hin left( 0,1right)$ has an infinitely
differentiable density on $left( 0,infty right)$. The proof of this
result is based on the techniques of the Malliavin calculus.
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